As discussed at this meeting by Silk, Wilkinson and Spergel, over the
next few years, increasingly more accurate measurements will be made
of the fluctuations in the cosmic microwave background (CMB)
radiation. The underlying physics governing the shape of the CMB
anisotropy spectrum can be described by the interaction of a very
tightly coupled fluid composed of electrons and photons before
recombination (e.g.,
Hu & White 1996;
Sunyaev & Zel'dovich
(1970).
Figure 6 shows a plot of the predicted
angular power spectrum for CMB anisotropies from
Hu, Sugiyama & Silk (1997),
computed under
the assumption that the fluctuations are Gaussian and adiabatic. The
position of the first angular peak is very sensitive to 0
(m + + k).

Figure 6. The angular power spectrum
of cosmic
microwave background anisotropies assuming adiabatic, nearly
scale-invariant models for a range of values of 0 and
(Hu, Sugiyama, and Silk
1997; their Figure 4).
The Cl values correspond to the squares of the
spherical harmonics
coefficients. Low l values correspond to large angular scales (l
~ 200° / ). The position
of the first acoustic
peak is predicted to be at l ~ 220 TOT-1/2, and
hence, shifts to smaller angular scales for open universes.

For information on cosmological parameters to be extracted from the
CMB anisotropies, the following must be true: first, the physical
source of these fluctuations must be understood, and second, the
sources of systematic error must be eliminated or minimized so that
they do not dominate the uncertainties.

Recently it has become clear that almost exact degeneracies exist
between various cosmological parameters (e.g.,
Efstathiou & Bond 1998;
Eisenstein, Hu &
Tegmark 1998)
such that, for example,
cosmological models with the same matter density can have the same CMB
anisotropies, while having very different geometries. As a result,
measurement of CMB anisotropies will, in principle, be able to yield
strong constraints on the products mh2 and
bh2, but not on the individual values of h (=
H0 / 100)
and m
directly. Hence, earlier suggestions that such
cosmological parameters could be measured from CMB anisotropies to
precisions of 1% or better (e.g.,
Bond, Efstathiou & Tegmark 1997)
will unfortunately not be realized. However, breaking these
degeneracies can be accomplished by using the CMB data in combination
with other data, for example, the Sloan survey and type Ia supernovae
(e.g. White 1999).

Currently the estimates of the precisions for which cosmological
parameters can be extracted from measurements of anisotropies in the
CMB are based on models in which the primordial fluctuations are
Gaussian and adiabatic, and for which there is no preferred scale.
Very detailed predictions can be made for this model, more so than for
competing models such as isocurvature baryons or cosmic strings or
textures. In the next few years, as the data improve, all of these
models will be scrutinized in greater detail.

Important additional constraints may eventually come from
polarization measurements (e.g.,
Zaldarriaga, Spergel &
Seljak 1997;
Kamionkowski et
al. 1997),
but these may require the next
generation of experiments beyond MAP and Planck. The polarization data
may provide a means of breaking some of the degeneracies amongst the
cosmological parameters that are present in the temperature data
alone. Furthermore, they are sensitive to the presence of a tensor
(gravity wave) contribution, and hence can allow a very sensitive test
of competing models.

Although it is not yet certain how accurately the cosmological
parameters can be extracted from measurements of CMB anisotropies,
what is clear is that upcoming, scheduled balloon and space
experiments offer an opportunity to probe detailed physics of the
early Universe. If current models are correct, the first acoustic
peak will be confirmed very shortly and its position accurately
measured by balloon experiments even before the launch of MAP. These
balloon experiments will soon be followed with the total sky and
multi-frequency coverage provided by MAP and Planck. This new era now
being entered, of precision CMB anisotropy experiments, is extremely
exciting.